Alright, what you're creating is called a Sample Space. It contains all possible combinations until you have enough information to rule combinations out. The abbreviations I'll be using are F for a fruit cup, E for eggs, B for a bagel, T for toast, and P for potatoes, and PA for pancakes. The sample would look like this:
E F T
E F B
E P T
E P B
PA F T
PA F B
PA P T
PA P B
Answer:
(a) ![\frac{dy}{dt}=-3\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D-3%5Cfrac%7B3%7D%7B4%7D)
(b) ![\frac{dx}{dt}=3\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D3%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
![x^{2} +y^{2}=25](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2By%5E%7B2%7D%3D25)
Take
of of each term.
![\frac{d}{dt}(x^{2})+\frac{d}{dt}(y^{2})=\frac{d}{dt}(25)\\\\(\frac{d}{dx}(x^{2})*\frac{dx}{dt}) +(\frac{d}{dy}(y^{2})*\frac{dy}{dt})=\frac{d}{dt}(25)\\\\2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%28x%5E%7B2%7D%29%2B%5Cfrac%7Bd%7D%7Bdt%7D%28y%5E%7B2%7D%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%2825%29%5C%5C%5C%5C%28%5Cfrac%7Bd%7D%7Bdx%7D%28x%5E%7B2%7D%29%2A%5Cfrac%7Bdx%7D%7Bdt%7D%29%20%2B%28%5Cfrac%7Bd%7D%7Bdy%7D%28y%5E%7B2%7D%29%2A%5Cfrac%7Bdy%7D%7Bdt%7D%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%2825%29%5C%5C%5C%5C2x%5Cfrac%7Bdx%7D%7Bdt%7D%20%2B2y%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%200%5C%5C%5C%5C)
For Question a
![2y\frac{dy}{dt}=-2x\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{-2x\frac{dx}{dt}}{2y} \\\\\frac{dy}{dt}=-\frac{x}{y}\frac{dx}{dt}](https://tex.z-dn.net/?f=2y%5Cfrac%7Bdy%7D%7Bdt%7D%3D-2x%5Cfrac%7Bdx%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdt%7D%3D%5Cfrac%7B-2x%5Cfrac%7Bdx%7D%7Bdt%7D%7D%7B2y%7D%20%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdt%7D%3D-%5Cfrac%7Bx%7D%7By%7D%5Cfrac%7Bdx%7D%7Bdt%7D)
Given that x = 3, y = 4, and dx/dt = 5.
![\frac{dy}{dt}=-\frac{3}{4}*5=-\frac{15}{4}\\ \\\frac{dy}{dt}=-3\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B4%7D%2A5%3D-%5Cfrac%7B15%7D%7B4%7D%5C%5C%20%20%20%5C%5C%5Cfrac%7Bdy%7D%7Bdt%7D%3D-3%5Cfrac%7B3%7D%7B4%7D)
For Question b
![2x\frac{dx}{dt}=-2y\frac{dy}{dt}\\\\\frac{dx}{dt}=\frac{-2y\frac{dy}{dt}}{2x} \\\\\frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}](https://tex.z-dn.net/?f=2x%5Cfrac%7Bdx%7D%7Bdt%7D%3D-2y%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B-2y%5Cfrac%7Bdy%7D%7Bdt%7D%7D%7B2x%7D%20%5C%5C%5C%5C%5Cfrac%7Bdx%7D%7Bdt%7D%3D-%5Cfrac%7By%7D%7Bx%7D%5Cfrac%7Bdy%7D%7Bdt%7D)
Given that x = 4, y = 3, and dx/dt = -5.
![\frac{dx}{dt}=-\frac{3}{4}*-5=\frac{15}{4}\\ \\\frac{dx}{dt}=3\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B4%7D%2A-5%3D%5Cfrac%7B15%7D%7B4%7D%5C%5C%20%20%20%5C%5C%5Cfrac%7Bdx%7D%7Bdt%7D%3D3%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
-3x - 3 <= 6
-3x <= 9
x >= -3
your answer options are not clear to me.
so, please pick the one corresponding to all x >= -3.
for any value of x greater or equal to -3 that inequality is true.
Answer:
12:45 PM
Step-by-step explanation:
First, add the time of the math class:
10:15 AM + 1 hour
= 11:15 AM
11:15 AM + 55 minutes
= 12:10 PM
Then, add the time of recess:
12:10 PM + 35 minutes
= 12:45 PM
So, her recess ends at 12:45 PM
Answer:
it's B
Step-by-step explanation:
Trust me